Parametric insurance for extreme risks: the challenge of properly covering severe claims

TL;DR

This paper analyzes the effectiveness of parametric insurance in covering extreme, heavy-tailed risks, highlighting potential deviations from actual losses and proposing supplementary mechanisms for large claims.

Contribution

It provides theoretical insights into the behavior of parametric insurance under heavy-tailed risks and emphasizes the role of nonlinear dependence measures for better risk coverage.

Findings

Heavy-tailed losses can cause significant deviations between actual loss and parameters.

Theoretical results quantify the mismatch in large claims, guiding supplement strategies.

Simulation shows nonlinear dependence improves protection across the distribution.

Abstract

Parametric insurance has emerged as a practical way to cover risks that may be difficult to assess. By introducing a parameter that triggers compensation and allows the insurer to determine a payment without estimating the actual loss, these products simplify the compensation process, and provide easily traceable indicators to perform risk management. On the other hand, this parameter may sometimes deviate from its intended purpose, and may not always accurately represent the basic risk. In this paper, we provide theoretical results that investigate the behavior of parametric insurance products when faced with large claims. In particular, these results measure the difference between the actual loss and the parameter in a generic situation, with a particular focus on heavy-tailed losses. These results may help to anticipate, in presence of heavy-tail phenomena, how parametric products should be supplemented by additional compensation mechanisms in case of large claims. Simulation studies, that complement the analysis, show the importance of nonlinear dependence measures in providing a good protection over the whole distribution.